- Associate Professor of Mathematics

**External address:**243 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2862

**Office Hours:**

Mondays, 3:30-5:00

Wednesdays, 10:30-12:00

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# James H. Nolen

**External address: **243 Physics Bldg, Durham, NC 27708**Internal office address: **Box 90320, Durham, NC 27708-0320**Phone: **(919) 660-2862**Office Hours: **
### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

I study partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. In many cases, the parameters for such equations are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in equations modeling random phenomena and whether one can describe the statistical properties of the solution to these equations. For example, I have worked on nonlinear partial differential equations that describe waves and moving interfaces in random media. This work involves ideas from both analysis and probability. I also study the asymptotic behavior of stochastic processes.

##### Education & Training

## Pages

## Mathematics

## Academics

## Current Students

## Future Students

- Associate Professor of Mathematics

Mondays, 3:30-5:00

Wednesdays, 10:30-12:00

partial differential equations, probability, asymptotic analysis, homogenization

asymptotic analysis

reactive diffusion equations & applications, homogenization of partial differential equations, random media, asymptotic analysis

asymptotic analysis

homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

Ph.D., University of Texas at Austin 2006

B.S., Davidson College 2000

Nolen, J. "Normal approximation for a random elliptic equation." *Probability Theory and Related Fields* 159.3-4 (2014): 661-700.
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Nolen, J. "Normal approximation for a random elliptic equation." *Probability Theory and Related Fields* (2013): 1-40.
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Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." *The Annals of Applied Probability* 23 (2013): 2238-2258. (Academic Article)
Full Text Open Access Copy

Nolen, J, Roquejoffre, J-M, Ryzhik, L, and Zlatoš, A. "Existence and Non-Existence of Fisher-KPP Transition Fronts." *Archive for Rational Mechanics and Analysis* 203.1 (2012): 217-246.
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Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "A short proof of the logarithmic Bramson correction in Fisher-KPP equations (Accepted)." *Networks and Heterogeneous Media* (2012). (Academic Article)

Matic, I, and Nolen, J. "A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation." *Journal of Statistical Physics* 149.2 (2012): 342-361.
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Mellet, A, and Nolen, J. "Capillary drops on a rough surface." *Interfaces and Free Boundaries* 14.2 (2012): 167-184.
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Cardaliaguet, P, Nolen, J, and Souganidis, PE. "Homogenization and Enhancement for the G-Equation." *Archive for Rational Mechanics and Analysis* 199.2 (2011): 527-561.
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Nolen, J, and Novikov, A. "Homogenization of the G-equation with incompressible random drift in two dimensions." *Communications in Mathematical Sciences* 9.2 (2011): 561-582.

Nolen, J. "An invariance principle for random traveling waves in one dimension." *SIAM Journal on Mathematical Analysis* 43.1 (2011): 153-188.
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120 Science Drive

117 Physics Building

Campus Box 90320

Durham, NC 27708-0320

phone: 919.660.2800

fax: 919.660.2821

dept@math.duke.edu